Find the derivative of $$\dfrac{x^n-a^n}{x-a}$$ for some constant a.

Asked by Pragya Singh | 1 year ago |  75

##### Solution :-

Let f(x) $$\dfrac{x^n-a^n}{x-a}$$

$$f'(x)=\dfrac{d}{dx}(\dfrac{x^n-a^n}{x-a})$$

By quotient rule,

$$\dfrac{(x-a)(nx^{n-1}-0)-(x^n-a^n)}{(x-a)^2}$$

$$\dfrac{nx^n-anx^{n-1}-x^n+a^n}{(x-a)^2}$$

Answered by Abhisek | 1 year ago

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